The listless waters of the Shatti Andulus Hotel beachfront offer quiet refuge these days for Idi Amin, Uganda's erstwhile president for life and Libyan leader Col. Musammar Qaddafi's hapless client.

Amin's exile here is officially denied but an executive jet, the target of insurance suits lodged by the new Kampala government, is parked on a Tripoli airstrip. And some of Amin's wives and children are seen occasionally playing in the Shatti Andulus pool under the watchufl eye of armed guards.

In a broad sense, the imbroglio caused by Amin is a symbol of Qaddafi's own garbled revolutionary credentials, another in a series of Tripoli's failings during the last decade to widen its influence in the Arab and African world.

Libya's involvement in Uganda "was a debacle, a costly misadventure that Qaddafi and the Libyans are trying to live down," siad one Western diplomat here. Beyond that, the envoy added, Uganda postively belied Qaddafi's image of successfully bankrolling liberation groups.

For Qaddafi, Uganda offered a foothold in black Africa - one ruled by a fellow Moslem who had turned against Israel and who was prepared to harbor anti-Israeli terrorists, as shown by the 1976 Entebbe incident.

For the Libyans, however, Amin's defeat cost more than wounded pride. At least 300 Libyan troops were killed while fighting for Amin and 54 were taken prisoner - serious losses in a country of only 2.7 million people.

Moreover, the Libyan armed forces, Qaddafi's principal source of political power, still are grousing over the disgraceful rout they suffered.

Adding to his difficulties, Qaddafi personally ordered U.S.-supplied Boeing 727s into the fray as military transport planes in violation of a recently signed accord, injecting unwanted tension into his already strained relations with the United States.

Such strains are viewed with concern in both Washington and Tripoli, for they threaten to upset a tenuously balanced relationship valued by both countries. While Libya's reputation for financing international terrorism is anathema to Washington, Tripoli remains the third largest supplier of U.S. oil imports. Conversely, although Qaddafi may rant against American Middle East policy and the Egyptian-Israeli peace treaty, his government receives more than $5 billion a year from the U.S. oil connection.

Libya's relationship with Amin seems harder to fathom, but the Ugandan is by no means out of place in the ideologically asymmetrical gazeteer of governments and political movements looking to Tripoli for patronage. They include the international terrorist Ilyich Ramires Sanchez, alias Carlos, the Philippines' Zamboangan Moslem separatists, Emperor Bokassa of the Central African Empire, the Irish Republican Army, the Japanese Red Army, Zimbabwe Rhodesia's Patriotic Front guerrillas, South Yemen and various Palestinian splinter groups.

Still, despite the undoubted expenditure of millions of dollars on such clients, including many who came in the name of Islam, Qaddafi's Libya remains isolated from the center of African and Arab politics.

"Libya is still way out. Everybody from Cairo to Baghdad thinks they are crazy," says former U.S. ambassador to Saudi Arabia James E. Akins.

An observer here offers a similar judgment: "The only way Libya has its way is if they pay; they're just not at the center of things."

This year Libya will earn an estimated $15.4 billion in oil revenues, nearly twice last year's income, leaving a substantial surplus on hand to underwrite any foreign adventure the colonel chooses. Most analysts expect that, as in the past, there will be a continuing gulf between Qaddafi's reputation as top checkwriter for international revolutionary movements and actual results.

"Everywhere you look you see big promises, but afterward you're likely to find disappointment," said a senior State Department official in Washington.

Qaddafi's most publicized aid for what he calls "liberation groups" is assistance to factions linked with terrorism.

Libya is now believed to be paying out $7 million to $8 million quarterly to the Palestinian movement, spread among eight groups including Fatah, the Democratic Front for the Liberation of Palestine, Dr. George Habash's Popular Front for the Liberation of Palestine, the pro-Syrian Saiqa and the Arab Liberation Front.

Libyan backing of radical groups such as Habash's is one of the major obstacles to improving ties with the United States.

During a meeting last month with Qaddafi's prime minister, Maj. Abdul Salaam Jalloud, Undersecretary of State David Newsom stressed this point. Asked about that meeting, Jalloud said, "There is lots of pressure for us to stop supporting the Palestinians."

Jalloud, like Qaddafi, rejects the notion that Libya supports terrorism. "If we are part of any movement using terrorism, we tell them it damages their cause," he said.

"But as a country we don't interfere [with groups] we aid," Jalloud said. "We give them help, They use the methods they want."

At the State Department, however, a senior official said that Libya has begun to moderate its posture slightly.

"In the last two years, we have seen no direct evidence of Libyan planning or financing terrorism," a State Department official said. "We also haven't seen any recent support of any kind for the IRA or the Japanese Red Army."

Carlos, the Venezuelan considered international terrorism's first citizen, also has not been seen in Libya for more than nine months, according to intelligence reports.

Qaddafi's long-standing record of links with terrorist groups, nevertheless, is remembered, especially in the United States.

One of the most publicized and for Qaddafi, politically costly, incidents took place in August 1976. Two Popular Front guerrillas flew from Libya to Istanbul to hijack an Israeli El Al flight. The raid, planned and executed by a group that Qaddafi still supports, was mounted in apparent retaliation for Israel's successful Entebbe operation, freeing Israeli hostages in Uganda.

In a burst of confusion that ended with bullets being sprayed through the Istanbul airport, four unarmed passengers were killed, including Harold W. Rosenthal, an aid to Sen. Jacob Javits (R-N.Y.).

A persistent and vocal critic of Qaddafi's backing for terrorist groups, Javits, the ranking minority member of the Senate Foreign Relations Committee, has continued to press the State Department to take a tough line against the Libyans.

Earlier this year Javits moved vigorously to block the sale of three Boeing 747s Quaddafi had contracted to buy. The plane sale, like earlier contracts signed for Lockheed C130s and Boeing 727s, has become a symbol of the freeze in U.S. relations with Libya.

Still, State Department officials see signs that Tripoli is slowly reversing its policies. It has signed all three major antihijacking accords and, sources said, is expected to extradite three Tunisians who hijacked an airliner earlier this year.

Another sign of moderation, sources said, is an order from Qaddafi to Col. Yunis Bilqasim, head of Libya's secret police, and the Libyan Army to cooperate with the West German officials tracking down members of the Bader-Meinhoff terrorist gang.

Security groups in Tripoli and Bonn are now linked by what one observer here calls "a good working channel."

Qaddafi aides also met with Italian officials who were trying to locate former Italian premier Aldo Moro after his kidnaping last year.

Asked whether Tripoli will change its position on supporting groups such as Habash's Popular Front, however, Jalloud answered bluntly: "Libya will not change."

While the details are often murky, Qaddafi's failure to follow through on aid commitments, is combined with the shortcomings of his personal diplomacy, explain some of the paradoxes of Libyan foreign policy.

Although Qaddafi is the most vocal pan-Arabist remaining among Middle Eastern heads of state, Libya is cut off from the center of Arab politics.

It was no surprise, for example, that the Arab summit talks convened to protest the Camp David accords were called by Iraq, not Libya. Qaddafi likewise has failed in successive attempts to unify Libya with other Arab countires.

Similarly, Qaddafi has frequently failed to meet his pledges to support other Arab states against Israel. The most recent example is that while promising $530 million at the Baghdad summit to aid Jordan, Syria and the Palestinians, Libya has paid out less than $25 million.

Adding to questions about Qaddafi's largesse, there is a story making the rounds of Arab capitals that Syrian President Hafez Assad was so affronted by Qaddafi's meager contribution that he ordered it sent back.

If true, it would not be the first time the colonel has failed to meet commitments to Syria. Some years ago Assad visited Moscow to negotiate arms purchases that Libya promised to finance, only to find out later that Tripoli had backed out.

Libya's revolutionary moves in Africa are likewise scrambled and dogged by contradictions.

For example, during the last decade Qaddafi has supported nearly every faction in a civil war in neighboring Chad. Most recently, he switched his backing from his favorite Moslem factions to ousted Christian president Felix Malloum and Waddel Kamougue, the so-called "butcher of Mondou."

Qaddafi has supported all the black nationalist factions in the Zimbabwe-Rhodesian war, including those of the Patriotic Front headed by Joshua Nkomo and Robert Mugabe.

Recently, however, Tripoli found itself in another embarrassing squeeze. The government regularly offers many of its liberation movement clients basic infantry training, usually for six-month stints, using Pakistani instructors and facilities in Libya.

But just as Libya was training a large detachment of guerrillas loyal to Bishop Abel Muzorewa, he joined former Hodesian premier Ian Smith's coalition government. The Libyans then sent all the guerrillas home.

Libya also has run into problems in its relations with neighboring Egypt. Quaddafi's often strained relations with President Anwar Sadat broke down entirely when Sadat launched his peace initiative with Israel. Since then, the open hostility between the two countries has taken them to the brink of war.

Sadat saves some of his favorite insults for Qaddafi, calling him "a child," and adding, "He thinks he is the second Napoleon."

In 1977, Qaddafi is widely rumored to have backed a Palestinian assassination squad bent on executing Sadat. The plot reportedly was discovered by Mossad, Isreal's intelligence service with details passed on to Sadat by order of Israeli Prime Minister Menachem Begin. The incident is said to have triggered Sadat's then inexplicable "weekend war," a series of retaliatory raids against Libya.

Ironically, Qaddafi's alleged plot may have been instrumental in pushing Sadat and Begin to the negotiating table.

After the peace accords were signed, Egypt moved more than 50,000 troops to the Libyan border and there has been a rapid exodus of Egyptian workers from Libya - totalling more than 100,000 in the past two years.

"Sadat could attack, but only if the U.S. asks him," said Jalloud.

Voicing Libyan fears that Washington is equipping Sadat as the region's new policeman - a role formerly played by the shah of Iran - Jalloud said, "We think the American arms for Sadat are for use against Libya."

U.S. officials deny this, but apprehensions persist.

Libyans believe that with 40 million Egyptians living at the edge of poverty, there are strong temptations for Cairo to reach across its border, annexing the oil-rich Sirte Basin.

Adding to the tensions, Libya's intelligence service has obtained what it says are copies of the Egyptian teneral staff's contingency plans to invade eastern Libya.

Meanwhile, Qaddafi moves ahead toward his long-held goal of having 100,000 Libyans under arms, and reportedly has strategically placed Soviet advisers along the Egyptian border as a "tripwire" - to discourage any potential Sadat-ordered invasion.

The quixotic colonel's propaganda campaign against Sadat also continues unabated. The Egyptian president is always referred to as "the humiliated and disgraced president." And when pictured in the media, Sadat is always shown with a glum, broken facial expression, with Moshe Dayan, wearing his eye patch, gleaming a sinister smile over his shoulder.

Next: The Revolution at Home. CAPTION: Picture 1, IDI AMIN...embarrassment to Qaddafi; Picture 2, Quaddafi sits between Palestinian guerrilla leaders Yasser Arafat, left, and Nayef Hawatmeh during a 1977 Arab summit, Gamma/Liaison; Picture 3, Tanzanian soldiers guard Libyan prisoners captured by Ugandan civilians while trying to flee country after the defeat of the Libyan-supported dictator, Idi Amin. William Campbell/Sygma; Picture 4, Quaddafi confers with Idi Amin, also in 1977. Quaddafi has been a supproter of the three. Associated Press; Map, no caption, By Richard Furno - The Washington Post